All categories

3 years ago

The angle bisectors of AXYZ are XG, YG, and ZG. They meet at a single point G.

Mathematics

1 answer:

Harrizon [31]3 years ago

3 0

Answer:

m∠FXD = 36°

EG = 10

m∠FZG = 24°

Step-by-step explanation:

In triangle XYZ, G is the incenter of the triangle.

Since, m∠FXG = 18°

And m∠FXD = 2(m∠FXG)

= 2 × 18°

= 36°

Since, point G is equidistant from all sides (Property of incenter of a triangle)

Therefore, DG = EG = GF = 10

Since, m∠X + m∠Y + m∠Z = 180°

2(m∠FXG) + m∠DYE + 2(m∠FZG) = 180°

2(18)° + 96° + 2(m∠FZG) = 180°

2(m∠FZG) = 180° - 132°

m∠FZG = 24°

You might be interested in

Which choice correctly expresses the number below in scientific notation?

nikklg [1K]

Answer:

Step-by-step explanation:

hjj

6 0

3 years ago

Zoe's pizza cost $12.99. She gave a tip of $2.00.

Flura [38]

I think its C , 15% but im not sure

5 0

3 years ago

What is the solution of the system? use a graph. check your answer. y=2x+4, y=x+2

vladimir1956 [14]

Answer:

see picture with work shown

4 0

3 years ago

JUST THE FIRST ONE EASY PLS ASAP

Sladkaya [172]

Answer:

<h2>For the first triangle, <u>x equals 22cm.</u></h2>

Here's how:-

x is the altitude or height of the triangle. To find it, we can use the Pythagoras theorem:-

$altitude^{2} + base^{2} = hypotenuse^{2}$

The base is 120cm and the hypotenuse is 122cm

Putting this in the equation, we get:-

$altitude^{2} + 120^{2} = 122^{2}$

$altitude^{2} = 122^{2}- 120^{2}$

$altitude^{2} = 14884 - 14400$

$altitude^{2}$ = 484

altitude = $\sqrt{484}$

<h3>altitude = 22cm</h3><h2><u>So, x = 22cm</u></h2>

7 0

3 years ago

There are 412 students and 20 teachers taking buses on a trip to a museum. Each bus can seat a maximum of 48. Which inequality g

-BARSIC- [3]

The inequality $\mathrm{b} \geq \frac{\text { total number of travelers }}{\text { capacity of each bus }}$ gives the least number of buses, b, needed for the trip. The least number of buses is 9

<u>Solution:</u>

Given that, There are 412 students and 20 teachers taking buses on a trip to a museum.

Each bus can seat a maximum of 48.

We have to find which inequality gives the least number of buses, b, needed for the trip?

Now, there are 412 students and 20 teachers, so in total there are 412 + 20 = 432 travelers

<em><u>The number of buses required “b” is given as:</u></em>

$\text { (b) } \geq \frac{\text { total number of travelers }}{\text { capacity of each bus }}$

$\text { So, number of buses required } \geq \frac{432}{48}$

Number of buses required ≥ 9 buses.

But least number will be 9 from the above inequality.

Hence, the inequality $\mathrm{b} \geq \frac{\text {total number of travelers}}{\text {capacity of each bus}}$ gives least count of busses and least count is 9.

6 0

3 years ago